A wire carrying current I has the shape shown in adjoining figure. [figure] Linear parts of the wire are very long and parallel to X-axis while semicircular portion of radius R is lying in Y-Z plane. Magnetic field at point O is
- B = - 0 I4 R ( i + 2 k )
- B = 0 I4 R ( i - 2 k )
- B = 0 I4 R ( i + 2 k )
- B = - 0 I4 R ( i - 2 k )
Answer
(1) B = - 0 I4 R ( i + 2 k )
Solution
Current enters along the wire at y = −R (flowing towards −x), goes round the semicircle and leaves along the wire at y = +R (flowing towards +x).
Each semi-infinite wire (O at perpendicular distance R from it, at its end): B1 = B2 = 0 I4 R
By the right-hand rule both are along - k B1 + B2 = - 0 I4 R(2 k)
Semicircle (in the Y-Z plane): B3 = 0 I4R = 0 I4 R , perpendicular to its plane, along - i
B = - 0 I4 R ( i + 2 k )
Answer: (1)